The formula
reaction = v × t · braking = v² ÷ (2 × μ × g)
Where it comes from
Stopping distance is two very different stretches. Reaction is proportional to speed: at twice the speed, twice the metres covered while your foot reaches the brake. Braking goes with the square, because what has to be shed is kinetic energy and that grows with the square of speed. So going from 50 to 100 does not double the total: it multiplies it by nearly three, which is exactly why an urban speed limit is not an arbitrary number.
How to work it out by hand
- Convert the speed from km/h to m/s by dividing by 3.6
- Multiply by the reaction time: those are the reaction metres
- Square the speed and divide by twice the grip times gravity
- Add the two stretches together
What is worth knowing
The grip coefficient is what the road surface contributes: 0.8 on dry asphalt, 0.5 wet, 0.25 on snow and 0.1 on ice. A gradient adds or subtracts: downhill, gravity pushes the car forward and lengthens the braking. The figure that surprises most is the speed halfway through the total distance: if at 100 km/h you need about seventy-seven metres, at the thirty-eight metre mark you are still doing more than eighty-eight, because most of those metres were reaction. A pedestrian who appears forty metres ahead is not a hard stop, it is an impact at almost full speed.